Father can't claim the child unless child lived in father's home more than half the year. You can't give a valid form 8332 release because you aren't a biological or legal parent or step parent (assuming you never married).
You can claim the child as a qualifying relative if the child lived in your home all 365 days of the year (or as a member of your household if you took a vacation, basically the child lives with you all 365 days). You don't need a form 8332 because that applies only to joint parents who live apart, and it would not be valid if you are not a legal or biological parent.
This creates a situation where, suppose the child lived in father's home for one night, and with you 364 nights, then no one can claim the child. Father can't because less than half the year and no one qualified to sign a form 8332, and you can't because less than the full year.
